Hereditary domination and independence parameters

• Autorzy: Wayne Goddard , Teresa Haynes , Debra Knisley
• Języki publikacji: EN

Abstrakty

EN

For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for arbitrary properties P that are closed under disjoint unions and subgraphs.

Słowa kluczowe

EN

domination; hereditary property; independence

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 2
• Strony: 239-248

Daty

wydano

2004

Twórcy

autor

Wayne Goddard

• Department of Computer Science, Clemson University, Clemson SC 29631, USA
• Department of Computer Science, University of Natal, Durban 4041, South Africa

autor

Teresa Haynes

• Department of Mathematics, East Tennessee State University, Johnson City TN 37614, USA

autor

Debra Knisley

• Department of Mathematics, East Tennessee State University, Johnson City TN 37614, USA

Bibliografia

• [1] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
• [2] M. Borowiecki, D. Michalak and E. Sidorowicz, Generalized domination, independence and irredundance, Discuss. Math. Graph Theory 17 (1997) 143-153, doi: 10.7151/dmgt.1048.
• [3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: Advances in Graph Theory (Vishwa, 1991) 41-68.
• [4] M.R. Garey and D.S. Johnson, Computers and Intractability (W H Freeman, 1979).
• [5] J. Gimbel and P.D. Vestergaard, Inequalities for total matchings of graphs, Ars Combin. 39 (1995) 109-119.
• [6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, 1997).
• [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds.) Domination in Graphs: Advanced topics (Marcel Dekker, 1997).
• [8] T.W. Haynes and M.A. Henning, Path-free domination, J. Combin. Math. Combin. Comput. 33 (2000) 9-21.
• [9] S.M. Hedetniemi, S.T. Hedetniemi and D.F. Rall, Acyclic domination, Discrete Math. 222 (2000) 151-165, doi: 10.1016/S0012-365X(00)00012-1.
• [10] D. Michalak, Domination, independence and irredundance with respect to additive induced-hereditary properties, Discrete Math., to appear.
• [11] C.M. Mynhardt, On the difference between the domination and independent domination number of cubic graphs, in: Graph Theory, Combinatorics, and Applications, Y. Alavi et al. eds, Wiley, 2 (1991) 939-947.

Identyfikatory

DOI

10.7151/dmgt.1228